Mixed integer programming models for fire fighting

Abstract

In this paper, a set of mixed integer programming (MIP) models to optimize the location of a set of resources when fighting fire is proposed. The MIP model integrates fire spread and the decisions relative to the resources location.Four problems are considered: protecting specific areas, minimizing the total burned area, and two problems of fire containment (depending on the definition of fire containment: no new ignitions in a given time interval or resources located in all the fire perimeter). A small example is used to illustrate the solutions to these problems.A transformation of the optimization problem of determining fire arrival times in a feasibility problem, based on linear programming duality, is also proposed. This transformation is used in all the MIP models, assuring the correctness of the fire arrival times in all the areas of the landscape.